Question

Compare the functions shown below:

f(x) = (x + 3)2 − 2
g(x)

linear graph with y intercept of negative 3 over 2 and x intercept of 3
h(x)

x y
−3 2
−2 7
−1 14
0 23
1 34
2 47
3 62
What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3?

Answer 1

For f (x):
f (x) = (x + 3) ^ 2 - 2
For x = -1
f (-1) = (-1 + 3) ^ 2 - 2
f (-1) = (2) ^ 2 - 2
f (-1) = 4 - 2
f (-1) = 2
For x = 3
f (3) = (3 + 3) ^ 2 - 2
f (3) = (6) ^ 2 - 2
f (3) = 36 - 2
f (3) = 34
AVR = ((34) - (2)) / ((3) - (- 1))
AVR = 8

For g (x):
linear graph with and intercept of negative 3 over 2 and x intercept of 3
y = mx + b
b = -3/2
For me we have:
0 = m (3) - 3/2
3m = 3/2
m = 1/2
The function g (x) is:
g (x) = (1/2) x - 3/2
For x = -1
g (-1) = (1/2) (- 1) - 3/2
g (-1) = -1/2 - 3/2
g (-1) = -4/2
g (-1) = -2
For x = 3
g (3) = (1/2) (3) - 3/2
g (3) = 3/2 - 3/2
g (3) = 0
AVR = ((0) - (- 2)) / ((3) - (- 1))
AVR = 1/2

For h (x):
Using the table we have:
AVR = ((62) - (14)) / ((3) - (- 1))
AVR = 12

from least to greatest:
1) g (x)
2) f (x)
3) h (x)

Answer:
The correct order of the functions from least to greatest is:
1) g (x)
2) f (x)
3) h (x)